Q. 34.7( 3 Votes )

The mean of the following frequency distribution of 200 observations is 332. Find the value of x and y.


Answer :

This is a grouped frequency distribution.


To find x and y, we’ll need to find mean of the following distribution by assumed mean method and equate it to the given mean of the following distribution, 332.


And class size, c = 50.


[ (150 – 100) = (200 – 150) = (250 – 200) = … = (550 – 500) = 50]


This given data is in exclusive type.


So, let’s construct a table finding midpoints and stating frequencies.



So now, we have


fiui = -130 – 3x


And fi = 146 + x + y = 200


Mean is given by



[given, mean = 332 and using the values from the table]




43 × 4 = 130 + 3x


172 = 130 + 3x


3x = 172 – 130


3x = 42



x = 14 …(i)


Since, there are 200 observations.


Sum of frequencies = 200 [Sum of frequencies depict total number of observation]


fi = 200


146 + x + y = 200


x + y = 200 – 146


x + y = 54 …(ii)


Putting the value of x from equation (i) into equation (ii), we get


x + y = 54


14 + y = 54


y = 54 – 14


y = 40


Thus, the missing frequencies are x = 14 and y = 40.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Best Method to Calculate Mean of Grouped DataBest Method to Calculate Mean of Grouped DataBest Method to Calculate Mean of Grouped Data48 mins
RD Sharma | Important Questions from Mode and MedianRD Sharma | Important Questions from Mode and MedianRD Sharma | Important Questions from Mode and Median36 mins
NCERT | Important Questions of StatisticsNCERT | Important Questions of StatisticsNCERT | Important Questions of Statistics44 mins
Smart Revision | Rapid Revision on StatisticsSmart Revision | Rapid Revision on StatisticsSmart Revision | Rapid Revision on Statistics59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses